Local Principal Component Analysis Research Articles

A new method to compute the principal components from self-organizing maps: an application to monsoon intraseasonal oscillations

The study develops a self-organizing map (SOM)-based local principal component analysis (PCA) to obtain the linearly decorrelated principal components (PCs) of monsoon intraseasonal oscillations (MISOs). Although the SOM-derived feature maps are not orthogonal like empirical orthogonal function (EOFs), we show that in the case of MISOs simple mathematical substitution can make the SOM-derived PCs linearly decorrelated to each other. Thus, the SOM-based local PCA is seen also to be statistically equivalent to extended EOF analysis when applied to MISO analysis. The life cycle and phase evolution of MISO through SOM-based PCA is robust and conforms to the results based on extended EOFs besides having potential to give new information. The remarkable similarity of results with the symmetric SOM configurations shows the effectiveness of these methods for use as empirical reduction models for climate patterns. The asymmetric SOM lattice configurations derive similar phase evolution as compared to a symmetric lattice, but asymmetric temporal evolutions in the PC-defined phase space. The results once again endorse the mathematical basis of PCA through SOM for geophysical applications.

Multiscale phase screen synthesis based on local principal component analysis

Motivated by the increasing importance of adaptive optics (AO) systems for improving the real resolution of large ground telescopes, and by the need of testing the AO system performance in realistic working conditions, in this paper we address the problem of simulating the turbulence effect on ground telescope observations at high resolution. The procedure presented here generalizes the multiscale stochastic approach introduced in our earlier paper [Appl. Opt. 50, 4124 (2011)], with respect to the previous solution, a relevant computational time reduction is obtained by exploiting a local spatial principal component analysis (PCA) representation of the turbulence. Furthermore, the turbulence at low resolution is modeled as a moving average (MA) process, while previously [Appl. Opt. 50, 4124 (2011)] the wind velocity was restricted to be directed along one of the two spatial axes, the use of such MA model allows the turbulence to evolve indifferently in all the directions. In our simulations, the proposed procedure reproduces the theoretical statistical characteristics of the turbulent phase with good accuracy.

A novel face feature descriptor using adaptively weighted extended LBP pyramid

This paper proposes a new face description with single sample by Adaptively Weighted Extended Local Binary Pattern Pyramid (AWELBPP). First, the proposed algorithm utilizes pyramid transform to represent sample image into multi-resolution images. Second, the multi-resolution images are divided into a set of horizontal sub-images. Then, Extended Local Binary Pattern (ELBP) is applied to the sub-images in order to calculate the Sub-ELBP pyramid and the local image entropy is employed to the sub-images for an adaptively weighting map (AWM) that can measure the importance of the information they contain. Finally, AWELBPP feature is extracted from the fusion of the Sub-ELBP pyramid and the AWM. Under different illumination, facial expression and partial occlusion conditions, simulated experiments and comparisons on many subsets of Yale face databases, Yale B face databases and ORL face databases show that the proposed algorithm is an outstanding method for single sample face recognition compared with local PCA, ELBP, CLBP, PLBP.

A novel identification system for counterfeit drugs based on portable Raman spectroscopy

Quick inspection methods for counterfeit drugs are of vital necessity. In this study, the feasibility of portable Raman spectroscopy as an analytical method together with a novel identification system for fake drugs detection is demonstrated. The rapid and convenient identification system based on modified local straight-line screening (LSLS) and principal component analysis (PCA) is developed to distinguish counterfeit from authentic. LSLS algorithm was originally designed to detect synthetic drug(s) adulterated in herbal medicines based on infrared spectroscopy. In order to adapt the LSLS method for the detection of the suspected counterfeit drugs based on portable Raman spectroscopy, modification of weighting is made in this paper to obtain the low false positive rate (FPR) and low false negative rate (FNR). The proposed identification system has been benchmarked by 7 kinds (40 batches) of hypoglycemic tablets and 12 common pharmaceutical excipients. The total sensitivity, specificity and accuracy are 96.77%, 97.48% and 96.35% respectively. The results indicate that the identification system is appropriate for the on-site preliminary screening of the suspected counterfeit drugs.

Identification of polo-like kinase 1 (PLK1) in aggressive prostate cancer by paradigm analysis.

5006 Background: Integrative analysis that combines expression data, copy number variation, sequence, and epigenetic data with thousands of known biological interactions can help identify strong biological associations and novel “genotype to phenotype” associations. Methods: We performed multi-dataset differential expression analysis with Statistical Analysis of Microarrays (SAM) and gene set enrichment analysis (GSEA) across 10 publicly-available PCa microarray datasets to identify genes and pathways differentially expressed between local (n=471) and metastatic (n=220) PCa. We used PARADIGM, an integrated pathway analysis method, on PCa tumor samples with mRNA expression, copy number variation, and TMPRSS2:ERG fusion status data to infer differential fusion gene-related “activities” for pathway features (genes, protein complexes, etc) within a “Superimposed Pathway” representing a comprehensive collection of genetic interactions currently containing 20,314 known interactions among 16,362 concepts representing 6916 proteins, 7345 complexes, 1449 families, 55 RNAs, 15 miRNAs and 582 processes. Results: Out of the 7571 genes tested (those genes having data in two or more studies), the meta-analysis on gene expression revealed 210 (1.8% FDR) positively associated with PCa metastasis and 403 (0.94% FDR) negatively associated genes (threshold was p<0.001, 2-tailed Student’s t-test). GSEA highlighted cell proliferation, cell cycle control, and DNA damage repair pathways with metastatic tumors. The PARADIGM analysis identified a network containing 914 features connected by 1137 edges. PLK1 was identified as both highly expressed in metastatic PCa and as one of the fourteen hubs in the largest (596-feature) sub-network identified by PARADIGM. PLK1 was also associated with high Gleason Sum and recurrent disease in independent local PCa datasets. Conclusions: Using an approach pioneered by members of our SU2C/PCF supported PCa Dream Team, integrated analysis across multiple PCa datasets associates PLK1 activity with aggressive PCa and suggests it may provide a novel treatment target for at least a genetic sub-set of advanced PCa.

Generalized incremental manifold learning algorithm based on local smoothness

Most of the existing manifold learning algorithms are not capable of dealing with new arrival samples.Although some incremental algorithms are developed via extending a specified manifold learning algorithm,most of them have some disadvantages more or less.In this paper,a new and more Generalized Incremental Manifold Learning(GIML) algorithm based on local smoothness was proposed.GIML algorithm firstly extracted the local smooth structure of data set via local Principal Component Analysis(PCA).Then the optimal linear transformation,which transformed the local smooth structure of new arrival sample's neighborhood to its correspondent low-dimensional embedding coordinates,was computed.Finally the low-dimensional embedding coordinates of new arrival samples were obtained by the optimal transformation.Extensive and systematic experiments were conducted on both artificial and real image data sets.The experimental results demonstrate that the GIML algorithm is an effective incremental manifold learning algorithm and outperforms other existing algorithms.

Double monitoring of common and specific features for multimode process

ABSTRACTA novel monitoring framework for multimode processes is proposed in this article. Generally, although the different modes have different process characteristics, they still share some common features, and the specific information is the unique characteristic that is not shared by all modes. On the basis of principal component analysis (PCA), a new statistical method, termed as local principal component analysis (LPCA), is developed for modeling multimode process data. LPCA is a modified version of PCA with the idea of maximizing local data variance, which aims to discover some directions that data, from all modes, share comparatively similar variance structure. In this low‐dimensional representation, the common features are captured and the residual corresponding to each mode can be treated as specific features. With the obtained LPCA model, both the common and specific features are utilized for monitoring. Moreover, a Bayesian inference strategy is further adopted to derive global indices of specific features for fault detection. Its feasibility and validity of the proposed method are illustrated through a simple multivariate linear system and the Tennessee Eastman challenge problem. © 2013 Curtin University of Technology and John Wiley & Sons, Ltd.

Extracting respiratory signals from thoracic cone beam CT projections

The patient respiratory signal associated with the cone beam CT (CBCT) projections is important for lung cancer radiotherapy. In contrast to monitoring an external surrogate of respiration, such a signal can be extracted directly from the CBCT projections. In this paper, we propose a novel local principal component analysis (LPCA) method to extract the respiratory signal by distinguishing the respiration motion-induced content change from the gantry rotation-induced content change in the CBCT projections. The LPCA method is evaluated by comparing with three state-of-the-art projection-based methods, namely the Amsterdam Shroud method, the intensity analysis method and the Fourier-transform-based phase analysis method. The clinical CBCT projection data of eight patients, acquired under various clinical scenarios, were used to investigate the performance of each method. We found that the proposed LPCA method has demonstrated the best overall performance for cases tested and thus is a promising technique for extracting a respiratory signal. We also identified the applicability of each existing method.

New Intelligent Computer Intrusion Detection Method Using Hessian Local Linear Embedding and Multi-Kernel Support Vector Machine

Computer networks frequently collapse under the destructive intrusions. It is crucial to detection hidden intrusions to protect the computer networks. However, a computer intrusion often distributes high dimensional characteristic signals, which increases the difficulty of intrusion detection. Literature review indicates that limited work has been done to address the nonlinear dimension reduction problem in computer intrusion detection. Hence, this study has proposed a new intrusion detection method based on the Hessian Local Linear Embedding (HLLE) and multi-kernel Support Vector Machine (SVM). The HLLE was firstly used to reduce the dimension of the original intrusion date in a nonlinear manner. Then the SVM with multiply kernels was employed to detect the intrusions. A real computer network experimental system has been established to evaluate the proposed method. Four typical intrusions have been tested. The test results show high effectiveness of the new detection method. In addition, the new method has been compared with the single-kernel SVM with Local Linear Embedding (LLE) or Principal Component Analysis (PCA). The comparison results demonstrate that the proposed HLLE plus multi-kernel SVM can provide the best computer intrusion detection rate of 97.1%.

Solving Partial Differential Equations on Point Clouds

In this paper we present a general framework for solving partial differential equations on manifolds represented by meshless points, i.e., point clouds, without parameterization or connection information. Our method is based on a local approximation of the manifold as well as functions defined on the manifold, such as using least squares, simultaneously in a local intrinsic coordinate system constructed by local principal component analysis using $K$ nearest neighbors. Once the local reconstruction is available, differential operators on the manifold can be approximated discretely. The framework extends to manifolds of any dimension. The complexity of our method scales well with the total number of points and the true dimension of the manifold (not the embedded dimension). The numerical algorithms, error analysis, and test examples are presented.

A local mesh method for solving PDEs on point clouds

In this work, we introduce a numerical method to approximate differential operators and integrals on point clouds sampled from a two dimensional manifold embedded in $\mathbb{R}^n$. Global mesh structure is usually hard to construct in this case. While our method only relies on the local mesh structure at each data point, which is constructed through local triangulation in the tangent space obtained by local principal component analysis (PCA). Once the local mesh is available, we propose numerical schemes to approximate differential operators and define mass matrix and stiffness matrix on point clouds, which are utilized to solve partial differential equations (PDEs) and variational problems on point clouds. As numerical examples, we use the proposed local mesh method and variational formulation to solve the Laplace-Beltrami eigenproblem and solve the Eikonal equation for computing distance map and tracing geodesics on point clouds.

A novel matrix-based method for face recognition

Two-dimensional principal component analysis (2DPCA) is one of the representative techniques for image representation and recognition. However, it fails in detecting the local variation of images, which characterizes the most important modes of variability of face images. Motivated by the fact that the local spatial geometric structure of images is effectual in learning the representative image space, we assign different weight to each training image and then present a novel method, namely local two-dimensional principal component analysis (L2DPCA), which explicitly considers the variations among nearby data. Finally, we describe an effective algorithm L2DPCA+2DPCA to further reduce dimensionality reduction. Extensive experimental results on two-face databases (Yale and AR) show the efficiency of the proposed method.

Local and global principal component analysis for process monitoring

In this paper, a novel data projection method, local and global principal component analysis (LGPCA) is proposed for process monitoring. LGPCA is a linear dimensionality reduction technique through preserving both of local and global information in the observation data. Beside preservation of the global variance information of Euclidean space that principal component analysis (PCA) does, LGPCA is characterized by capturing a good linear embedding that preserves local structure to find meaningful low-dimensional information hidden in the high-dimensional process data. LGPCA-based T2 (D) and squared prediction error (Q) statistic control charts are developed for on-line process monitoring. The validity and effectiveness of LGPCA-based monitoring method are illustrated through simulation processes and Tennessee Eastman process (TEP). The experimental results demonstrate that the proposed method effectively captures meaningful information hidden in the observations and shows superior process monitoring performance compared to those regular monitoring methods.

MG-local-PCA method for reduced order combustion modeling

Chemistry tabulation techniques such as flamelet models are a popular way to account for detailed chemistry effects in numerical simulation. These techniques are based on the identification of a low dimensional manifold in chemical space that accurately represents chemical evolutions associated to a specific combustion regime. During the last years, several authors used the Principal Component Analysis (PCA) to identify low dimensional manifold for combustion problems. However, full coupling between this manifold and flow solver has not yet been performed to the authors knowledge. The present paper introduces a new approach called Manifold Generated by a Local PCA or MG-L-PCA, which fully couple the manifold identified by a PCA and a DNS flow solver. The first part of the paper presents the PCA approach. Then, the coupling between this manifold and a DNS solver is presented. The MG-L-PCA approach is finally validated against a DNS simulation of flame vortex interaction using both detailed mechanism and a FPI manifold. Unlike FPI, the MG-L-PCA reproduces the dispersion in the chemical space induced by the flame-vortex interaction both for the species and the source terms.

A facial sparse descriptor for single image based face recognition

Single image based face recognition under different variations such as occlusion, expression and pose has been recognized as an important task in many real-world applications. The popularly widely used holistic features are easily distorted due to occlusion and some other variations. In order to tackle this problem, the sparse local feature descriptor based recognition methods have become more and more important, and promising performance is obtained. The recently developed SIFT, which detects feature points sparsely and extracts feature locally for object matching between different views and scales, can also benefit single image based face recognition. However, we find in this paper that SIFT should not be directly used for face recognition, because face recognition differs from generic object matching. To this end, we develop a new framework for detecting feature keypoints sparsely, describing feature context and matching feature points between two face images. We call this new proposed framework as Facial Sparse Descriptor (FSD). Experiments are conducted to support our analysis of SIFT, and extensive experiments are also presented to validate the proposed FSD against SIFT and its two variants, two dense local feature descriptor (i.e., LBP and HoG), PCA and Gabor based methods on AR, CMU and FERET databases.

Some refinements of the standard autoassociative neural network

Improving the training algorithm, determining near-optimal number of nonlinear principal components (NLPCs), extracting meaningful NLPCs, and increasing the nonlinear, dynamic, and selective processing capability of the standard autoassociative neural network are the objectives of this article that are achieved independently by some new refinements of the network structure and the training algorithm. In addition, three different topologies of the network are presented, which make it possible to perform local nonlinear principal component analysis. Performances of all methods are evaluated by a stock price database that demonstrates their efficiency in different situations. Finally, as it will be illustrated in the last section, the proposed structures can be easily combined together, which introduce them as efficient tools in a wide range of signal processing applications.

Sharp feature extraction in point clouds

Sharp feature extraction has been playing an important role in point cloud processing. In this study, a novel method for extracting sharp features from point clouds is presented. It is proposed that in a given point cloud, the displacement between each of the points and the weighted average position in the given neighbourhood of that point is calculated, and the point is labelled as the candidate sharp feature point if the displacement is salient. The normal directions of the obtained candidate sharp feature points are estimated by means of local principal component analysis. Tensor voting is performed to refine the normal estimates. The displacement between a point and its locally weighted average position is projected along the estimated normal direction. The points with extreme projection values are defined as the final sharp feature points. The implementation of the proposed method on both synthesised and practical scanned point clouds show that the method is effective and robust for the purpose of sharp feature extraction.

Novel dynamic Bayesian networks for facial action element recognition and understanding

In daily life, language is an important tool of communication between people. Besides language, facial action can also provide a great amount of information. Therefore, facial action recognition has become a popular research topic in the field of human-computer interaction (HCI). However, facial action recognition is quite a challenging task due to its complexity. In a literal sense, there are thousands of facial muscular movements, many of which have very subtle differences. Moreover, muscular movements always occur simultaneously when the pose is changed. To address this problem, we first build a fully automatic facial points detection system based on a local Gabor filter bank and principal component analysis. Then, novel dynamic Bayesian networks are proposed to perform facial action recognition using the junction tree algorithm over a limited number of feature points. In order to evaluate the proposed method, we have used the Korean face database for model training. For testing, we used the CUbiC FacePix, facial expressions and emotion database, Japanese female facial expression database, and our own database. Our experimental results clearly demonstrate the feasibility of the proposed approach.

Computerized scar detection on renal cortical scintigraphy images

Renal cortical scintigraphy is a well-established functional imaging technique for visual analysis of radiopharmaceutical tracer distribution. However, the visual evaluation is subjective, causing interobserver variability, especially in a quantifiable number of scars. The purpose of this study was to develop new computerized methods in renal cortical scintigraphy image interpretation, particularly addressing activity distribution and cortex continuity (scars). The proposed methods involve preprocessing stages of model-based automatic kidney segmentation using active-shape model and image normalization (transforming each kidney image into a standardized image vector). For our previous computer-aided diagnosis scheme, two new image-based features [localized activity drop and principal component analysis (PCA)] were defined. Their performance was evaluated and compared with our previous scheme by using free-response receiver operating characteristic that is in terms of sensitivity (true-positive fraction) and the mean number of false positives (FPs) per image. Clinical tests were conducted in 297 patients (231 normal and 66 abnormal). The PCA-based image feature presented the best scar detection performance, followed by the localized activity drop feature. Both schemes were found to be superior to our previous computer-aided diagnosis scheme. In the PCA-based scheme, for sensitivity of 0.90 (76/84), the mean number of FPs was measured as 4.52 (1343/297). For another setting with reduced sensitivity of 0.79 (66/84), the mean number of FPs improved to 1.21 (360/297). Finally, a decision fusion scheme using 'majority voting' was also proposed, the sensitivity and mean number of FPs of which were measured as 0.83 (70/84) and 1.90 (563/297), respectively. The proposed methods have potential to provide effective second-reader information to nuclear medicine specialists in finding scar regions. Possible ways to improve the FP rate were also proposed.

Improving Performance and Accuracy of Local PCA

Local Principal Component Analysis (LPCA) is one of the popular techniques for dimensionality reduction and data compression of large data sets encountered in computer graphics. The LPCA algorithm is a variant of k-means clustering where the repetitive classification of high dimensional data points to their nearest cluster leads to long execution times. The focus of this paper is on improving the efficiency and accuracy of LPCA. We propose a novel SortCluster LPCA algorithm that significantly reduces the cost of the point-cluster classification stage, achieving a speed-up of up to 20. To improve the approximation accuracy, we investigate different initialization schemes for LPCA and find that the k-means++ algorithm [[AV07]] yields best results, however at a high computation cost. We show that similar ideas that lead to the efficiency of our SortCluster LPCA algorithm can be used to accelerate k-means++. The resulting initialization algorithm is faster than purely random seeding while producing substantially more accurate data approximation.